First we need to go to the site "sui-names.com". Next, attach your wallet by clicking on Connect Wallet.
Write any name, press Enter. If the name is free, click will be on Claim. Sign in the wallet.
If the process is successful, the Activate name button will appear. To get the transaction, you need to click on it. If the name is activated, the Disable name button will appear.
That's it, now you are the owner of a domain name in the SUI test network.